A Probabilistic Framework to Obtain a Common Labelling between Attributed Graphs

The computation of a common labelling of a set of graphs is required to find a representative of a given graph set. Although this is a NP-problem, practical methods exist to obtain a sub-optimal common labelling in polynomial time. We consider the graphs in the set have a Gaussian distortion, and so, the average labelling is the one that obtains the best common labelling. In this paper, we present two new algorithms to find a common labelling between a set of attributed graphs, which are based on a probabilistic framework. They have two main advantages. From the theoretical point of view, no additional nodes are artificial introduced to obtain the common labelling, and so, the structure of the graphs in the set is kept unaltered. From the practical point of view, results show that the presented algorithms outperform state-of-the-art algorithms.